$Withionmove

When the system has ion to perform as drift-diffusion equations, we solve the time dependent drift-diffusion for slow ion move simulation. Since the ion moves may not be governed fermi-level concept. We simply treat is a tradiational drift-diffusion equations.

$\frac{\partial M_{ion}}{\partial t} = \nabla \left( (q_{sign}) e\mu M_{ion} \vec{E} - q D_{M} \nabla M_{ion} \right)$

Ideally, the ion density is given by initial setting. The total ion number should be fixed. The program is aim to model multi-ions drift-diffusion. The command is as following.

$Withionmove
$N_{sweep}$ $N_{output}$
Sweep_type_1  $T_{1,stop}$  $dt_{1}$ P1 P2 P3 P4 P5 ...
Sweep_type_1  $T_{2,stop}$  $dt_{2}$ P1 P2 P3 P4 P5 .. 
 ... 
 ...
Sweep_type_N_{sweep  $T_{N_{sweep},stop}$  $dT_{M_{sweep}}$  P1 P2 P3 P4 P5 ..
$N_{ions} ~~ q_{sign,1} ~~ q_{sign,2} ~~ q_{sign,3}  ....~~ q_{sign,N_{ions}}$
$P_{type,1} ~~ M_{ions,1} \mu$ p3 p4 Parameters of the 1 layer
$P_{type,2} ~~ M_{ions,2} \mu$ p3 p4 Parameters of the 2 layer
$P_{type,3} ~~ M_{ions,3} \mu$ p3 p4 Parameters of the 3 layer
 ....
 .....
$P_{type,N} ~~ M_{ions,N} \mu$ p3 p4 Parameters of the $totalregion layer

$N_{sweep}$: The number of runs for the time step
$N_{output}$: The number of output results for each run
Sweep_type:
1: constant voltage, P1 to P5 is not used
2: Sweep Vg during this time period P1=Vgstart, P2=Vgend, P3=swdt of each step  (step Number=  $T_{1,stop}/swdt$
3: Sweep Vd during this time period P1=Vdstart, P2=Vdend, P3=swdt of each step 
4,5,6.... leave for future use
$T_{1,stop}$ : The time for the first run. $T_{2,stop}$The time for the 2nd run. 
$dt_{1}$ is the $\delta t$ for each sweep. 
$N_{ions}$ How many ions are considered. If we only want to consider 1 negative ion,we can put 1
$q_{sign}$ The sign of ions. only accept $\pm 1.0$

For example: Consider 2 ions, 1st is negative charges, 2nd is positive charges, total 5 Regions we can

$Withionmove
3 1000
1 1.00  1.0d-4 
3 1.00  1.0d-4 0.0 1.0 0.02  
1 1.00  1.0d-4
2 -1.0 1.0
1 0.0e17 0.0      0.0e17 0.0   
1 1.0e17 1.0e-11  2.0e17 1.0e-12
1 1.0e17 1.0e-11  2.0e17 1.0e-12
1 1.0e17 1.0e-11  2.0e17 1.0e-12
1 1.0e17 1.0e-11  2.0e17 1.0e-12

$P_{type,1}$ is the parameter type:  it depends on ion number $N_{ions}$
1: $M_{ions,1} ~~~\mu$, $M_{ions,2} ~~~\mu$,........ $M_{ions,N_{ions}}, ~~~\mu_{N_{ions}}$
2: $M_{ions,1} ~~~\mu ~ D_{M}$, $M_{ions,2} ~~~\mu~~D_{M}$,........ $M_{ions,N_{ions}}, ~~~\mu_{N_{ions}}~~ D_{M}$

When type 1 is chosen, we only put mobility $\mu$, and the diffusion coefficient $D_{M}$ is calculated with Einstein relation, where

 $D_{M} = \mu k_{B} T / q$